Principal - September/October 2019 - 42

PRACTITIONER'S CORNER

3 Ways to Support Problem-Based
Instruction
Allowing students to find solutions on their own enhances mathematics learning
By William G. McCallum

W

hen I was a child, I enjoyed
borrowing puzzle books from
the library. One puzzle was "The
12-Coin Problem"-the most difficult
of all coin-weighing problems. My
mother and I tackled the problem at
the same time, but we worked on it
separately. She solved it first. I tried
and tried, but I couldn't come up with
a solution. Later that evening, she
found me in my room, in tears. "Do
you want me to tell you the solution?"
she asked. I said no. I'll always remember the joy I felt when I finally figured
it out later that night.
Looking back at that experience,
it's no surprise that I went on to
become a mathematician. But can all
students experience the elation I felt
at solving a difficult problem? Is that
really the best way to help students

42

Principal n September/October 2019

learn mathematics? Research says
yes. The National Academies' publication "How People Learn" shows
that learning is more robust if students have a chance to grapple with
a problem before hearing explicit
instruction on it. Both components-and the order in which they
happen-are important.
Try and Try Again

Implementing problem-based instruction in mathematics classrooms means
believing all students can solve problems on their own and giving them a
chance to try. Here are a few ways to
support students in their efforts, without giving away the ending:
1. Cultivate positive attitudes about
effort. One of the first steps in

implementing a problem-based
approach in the classroom is
cultivating the right attitudes
and beliefs. Many students-and
parents-think that mathematical knowledge and skills belong
exclusively to "math people."
Yet research shows that students
who believe that effort is more
important than innate talent
learn more.
In the words of the National
Research Council report "Adding
It Up," we want students to
develop a "productive disposition-[the] habitual inclination
to see mathematics as sensible,
useful, and worthwhile, coupled
with a belief in diligence and
one's own efficacy." Give students
the opportunity, time, and space
www.naesp.org


https://www.doi.org/10.1023/A:1018318822120 http://www.naesp.org

Principal - September/October 2019

Table of Contents for the Digital Edition of Principal - September/October 2019

From the Editor
Snapshots
5 Things
Getting to Why
A Brighter Future for Personalized Learning
Models of Voice and Choice
When Rural Gets Personal
Research Roundup: The Personal Touch
New Sensation
The Language of Learning
Giving Back, Together
In the Spotlight
Practitioner’s Corner
Early Career
Raising the Bar
The Reflective Principal
Speaking Out
Parents & Schools
NAESP Partners & Advertiser Index
Principal - September/October 2019 - Cover1
Principal - September/October 2019 - Cover2
Principal - September/October 2019 - 1
Principal - September/October 2019 - 2
Principal - September/October 2019 - 3
Principal - September/October 2019 - From the Editor
Principal - September/October 2019 - 5
Principal - September/October 2019 - Snapshots
Principal - September/October 2019 - 7
Principal - September/October 2019 - 5 Things
Principal - September/October 2019 - 9
Principal - September/October 2019 - Getting to Why
Principal - September/October 2019 - 11
Principal - September/October 2019 - 12
Principal - September/October 2019 - 13
Principal - September/October 2019 - 14
Principal - September/October 2019 - 15
Principal - September/October 2019 - A Brighter Future for Personalized Learning
Principal - September/October 2019 - 17
Principal - September/October 2019 - 18
Principal - September/October 2019 - 19
Principal - September/October 2019 - Models of Voice and Choice
Principal - September/October 2019 - 21
Principal - September/October 2019 - 22
Principal - September/October 2019 - 23
Principal - September/October 2019 - When Rural Gets Personal
Principal - September/October 2019 - 25
Principal - September/October 2019 - 26
Principal - September/October 2019 - 27
Principal - September/October 2019 - Research Roundup: The Personal Touch
Principal - September/October 2019 - 29
Principal - September/October 2019 - New Sensation
Principal - September/October 2019 - 31
Principal - September/October 2019 - The Language of Learning
Principal - September/October 2019 - 33
Principal - September/October 2019 - 34
Principal - September/October 2019 - 35
Principal - September/October 2019 - Giving Back, Together
Principal - September/October 2019 - 37
Principal - September/October 2019 - 38
Principal - September/October 2019 - 39
Principal - September/October 2019 - In the Spotlight
Principal - September/October 2019 - 41
Principal - September/October 2019 - Practitioner’s Corner
Principal - September/October 2019 - 43
Principal - September/October 2019 - Early Career
Principal - September/October 2019 - 45
Principal - September/October 2019 - Raising the Bar
Principal - September/October 2019 - 47
Principal - September/October 2019 - The Reflective Principal
Principal - September/October 2019 - 49
Principal - September/October 2019 - 50
Principal - September/October 2019 - 51
Principal - September/October 2019 - Speaking Out
Principal - September/October 2019 - 53
Principal - September/October 2019 - Parents & Schools
Principal - September/October 2019 - NAESP Partners & Advertiser Index
Principal - September/October 2019 - 56
Principal - September/October 2019 - Cover3
Principal - September/October 2019 - Cover4
https://www.nxtbook.com/ygsreprints/NAESP/principal_20201112
https://www.nxtbook.com/ygsreprints/NAESP/principal_20200910
https://www.nxtbook.com/ygsreprints/NAESP/principal_20200506
https://www.nxtbook.com/ygsreprints/NAESP/principal_20200304
https://www.nxtbook.com/ygsreprints/NAESP/principal_20200102
https://www.nxtbook.com/ygsreprints/NAESP/principal_wallacesup_20200102
https://www.nxtbook.com/ygsreprints/NAESP/principal_20191112
https://www.nxtbook.com/ygsreprints/NAESP/principal_Crayolasup_20190910
https://www.nxtbook.com/ygsreprints/NAESP/principal_20190910
https://www.nxtbook.com/ygsreprints/NAESP/principal_20190506
https://www.nxtbook.com/ygsreprints/NAESP/principal_wallace_20190304
https://www.nxtbook.com/ygsreprints/NAESP/principal_20190304
https://www.nxtbook.com/ygsreprints/NAESP/principal_20190102
https://www.nxtbook.com/ygsreprints/NAESP/principal_20181112
https://www.nxtbook.com/ygsreprints/NAESP/principal_supplement_20181112
https://www.nxtbook.com/ygsreprints/NAESP/principal_Crayolasup_20180910
https://www.nxtbook.com/ygsreprints/NAESP/principal_20180910
https://www.nxtbook.com/ygsreprints/NAESP/principal_wallacesupp_20180506
https://www.nxtbook.com/ygsreprints/NAESP/principal_20180506
https://www.nxtbook.com/ygsreprints/NAESP/principal_20180304
https://www.nxtbook.com/ygsreprints/NAESP/principal_mottsupp_20180102
https://www.nxtbook.com/ygsreprints/NAESP/principal_20180102
https://www.nxtbook.com/ygsreprints/NAESP/principal_20171112
https://www.nxtbook.com/ygsreprints/NAESP/principal_20170910
https://www.nxtbook.com/ygsreprints/NAESP/principal_crayolasupp_20170910
https://www.nxtbook.com/ygsreprints/NAESP/principal_20170708
https://www.nxtbook.com/nxtbooks/manifest/principal_20170304
https://www.nxtbook.com/nxtbooks/manifest/principal_20170102
https://www.nxtbook.com/nxtbooks/manifest/principal_20161112
https://www.nxtbook.com/nxtbooks/manifest/principal_crayolasupp_20160910
https://www.nxtbook.com/nxtbooks/manifest/principal_20160910
https://www.nxtbookmedia.com